M1311689 Mersenne number exponent details

Residue

Status

L-L

11FB04B08C202673

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	22.6532	68.6567%	500000	15000000	0.0593	4.8686%	22.7125	70.1827%	1.5260%
PrimeNet	2⁵⁶	0.0073	62.5000%	6000	100000	0.0005	2.5982%	0.0078	63.4743%	0.9743%
GPU72	2⁶⁰	0.1171	65.0000%	5500	40000	0.0003	0.9752%	0.1174	65.3413%	0.3413%
Difference	+7	+22.5361	+3.6567%	+494500	+14960000	+0.0589	+3.8934%	+22.5950	+4.8414%	+4.8414%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.6532

68.6567%

500000

15000000

0.0593

4.8686%

22.7125

70.1827%

1.5260%

PrimeNet

2⁵⁶

0.0073

62.5000%

6000

100000

0.0005

2.5982%

0.0078

63.4743%

0.9743%

GPU72

2⁶⁰

0.1171

65.0000%

5500

40000

0.0003

0.9752%

0.1174

65.3413%

0.3413%

Difference

+22.5361

+3.6567%

+494500

+14960000

+0.0589

+3.8934%

+22.5950

+4.8414%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1311689	12531880217312940277543687069843369	35	113.271	4777001338470071898728923956 2² × 3² × 7 × 101 × 257 × 563 × 967 × 1783 × 128819 × 5840287	2014-06-03	128819	5840287	1.415e+11	0.0202	0.0273

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1311689

12531880217312940277543687069843369

113.271

4777001338470071898728923956
2² × 3² × 7 × 101 × 257 × 563 × 967 × 1783 × 128819 × 5840287

2014-06-03

128819

5840287

1.415e+11

0.0202

0.0273

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	eteo	v4_computers	200000	2000000		-		-	-	0.014	-	-	2.779%
2014-06-03T07:04:00	mikr	MSI	500000	15000000			12531880217312940277543687069843369	35	113.271	0.059	0.083	0.119	4.869%
2016-03-17T19:04:48	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 12531880217312940277543687069843369	-	-	0.059	-	-	4.869%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:10	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.088	-	-
2009-02-14T15:55:00	Sturle Sunde	ghirardelli.ifi	2⁶⁰	2⁶¹		-	-	0.117	-	-
2011-05-09T14:43:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.234	-	-
2013-01-07T13:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.748	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.817 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	20.817 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	9.70
250000	35000000		50	11.12

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-15T02:26:00	Steve Scott	Abit	50000	5000000						1	0.039
2008-09-05T22:02:00	Sturle Sunde	v23	50000	5000000						3	0.116
2009-02-19T00:14:00	Sturle Sunde	v21	50000	5000000						3	0.116
2009-07-21T04:53:00	SubPrime	c2d0	50000	5000000						3	0.116
2009-11-03T02:45:00	James Hintz	19_101609	50000	5000000						3	0.116
2010-04-29T19:21:00	sannerud.com	snap2	50000	5000000						3	0.116
2011-02-04T13:09:00	greensinoz	giopa01	50000	5000000						3	0.116
2011-11-07T02:05:00	Oscar Östlin		50000	5000000						1	0.039
2012-02-08T07:45:00	unconnected	can-01	50000	5000000						3	0.116
2012-09-06T13:35:00	OS1	Tina	50000	5000000						3	0.116
2013-07-15T04:35:00	zampel	dufay	50000	5000000						3	0.116
2014-01-22T03:31:00	OS1	Tina	50000	5000000						3	0.116
2014-03-09T01:32:00	Bruce	snowflake	50000	5000000						3	0.116
2018-05-18T10:15:05	TJAOI	Manual testing	50000	5000000						216	8.346
2021-07-30T10:24:15	TJAOI	Manual testing	250000	35000000						50	11.12

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront